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andrew-mc [135]
3 years ago
14

The diagram shows two parallel lines and transversal. If the measure of <6 is 140, what is the measure of <1?

Mathematics
2 answers:
alexandr402 [8]3 years ago
5 0
Angles 6 and 3 are supplementary.  If angle 6 is 140, then angle 3 is 40.  Because those lines are parallel and cut by a transversal, then angles 3 and 1 are corresponding and congruent.  That means that angle 1 measures 40° also.  Choice D.
VladimirAG [237]3 years ago
3 0

Answer:

(D)

Step-by-step explanation:

Given: It is given that ∠6 measures 140°.

To find: The measure of ∠1.

Solution:

It is given that ∠6 measures 140° and since there are two parallel lines which are cut by a transversal, then using the properties of parallel lines, we have

m∠6=m∠2(Alternate interior angles)

Therefore, m∠6=m∠2=140°

Also, m∠2 and m∠1 forms the linear pair, therefore

m∠1+m∠2=180°(Linear pair)

⇒m∠1+140°=180°

⇒m∠1=180-140

⇒m∠1=40°

Thus, the measure of ∠1 is 40°.

Hence, option D is correct.

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4 0
3 years ago
Alicia, Quentin, and Rosalyn are siblings. Alicia is the oldest sibling. Quentin is four years younger than Alicia. Rosalyn is t
tatiyna

Answer:

Alicia is 18years

Quentin is 14years

Rosalyn is 16years

Step-by-step explanation:

Let the age of Alicia be x

Let the age of Quentin be y

Let the age of Rosalyn be z

If the sum of the siblings’ ages, in years, is 48 then;

x+y+z = 48.... 1

If Rosalyn is two years older than Quentin then;

z =y+2 ..... 2

Also if Quentin is four years younger than Alicia then;

y = x-4 ... 3

From 3:

x = y+4 ... 4

Substitute 2 and 4 into 1 to have:

y+4+y+y+2 = 48

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2 years ago
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